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This module will see you develop and extend your knowledge of methodology to understand functions in a more formal sense especially by analysing infinite series and convergence.

Your studies will be complimented by using practice and technique, leading to a more rigorous treatment.

You'll combine the theory of matrices and vector spaces with practical problem solving and computation.

You'll meet several abstract notions such as basis and orthogonality and use them to develop powerful methods which can then be applied to further equations and functions.

You'll analyse systems that will help to make future predictions for a number real-world processes; from predicting data and operational research.

Through difference and differential equations you'll discover how to make sure your mathematical findings are relevant to other sectors and industries.

Statistical methodology will see you probe data, make decisions and develop computing skills using python.

You'll take part in hands-on sessions to see the theory to highlight your problem-solving abilities.

While you'll see the theoretical side to this topic, problem-solving and hands-on sessions will be the main activity.

You'll model an issue drawn from live, open-ended problems, identify and implement practical methods to analyse and solve your chosen problem, then produce reports to communicate your analysis professionally. You'll also work with careers guidance to relate your skills and interests to opportunities, and recognise how to best present yourself in effective applications and interviews.

Determining vector calculus gradients, divergences and curls, you will evaluate line, surface and volume integrals, apply integral theorems, find Fourier series, solve differential equations analytically and interpret solutions.

You'll look at sequences and series, construct proofs and counter-examples, and look at the differentiation and integration of real and complex functions. You'll emerge from this module able to define and apply theorems, illustrate complex mappings, understand properties of standard complex functions, and use techniques like evaluating derivatives/integrals to solve problems.

In this module, you'll study the methods used to build supervised and unsupervised machine learning models. Combining traditional pen-and-paper mathematics with powerful computational methods, you'll train machine learning models to fit parameters, learn patterns, and make predictions.

You'll formulate and solve linear and non-linear programming models, applying your skills to operational research problems, and prepare for advanced modelling studies in simulation, forecasting and other forms of planning.

You'll construct group theory proofs and show counterexamples. explore modular arithmetic and Euclidean division, and build your toolkit for your final year studies in modern algebra.

You'll apply creative mathematical and programming methods to model and analyse financial problems. Through simulations of finance scenarios, you'll examine and address practical questions in advanced market dynamics.

First, you'll master analytical mechanics using Lagrangian and Hamiltonian techniques, reducing complex systems into simpler, symmetric forms. Then you'll analyse chaotic dynamics with differential and difference equations. When you complete the module, you'll have developed lasting intuition and problem-solving agility, with a versatile toolkit of theory and techniques essential for any physics career.

In this module, you'll learn to formulate and communicate problems in statistical terms, study estimation and sampling, and interpret the results of advanced models and experiments.

You'll study heat, wave and Laplace equations, with applications in science.

Adapting to the school environment, you'll explore STEM themes with classes from Key Stage 3 to Sixth Form, before reflecting critically on teaching practices. Through this mentorship of mathematics and physics teachers, you'll get direct experience of STEM education, break down stereotypes of mathematics, and prove your ability to communicate difficult concepts.

You'll study multiple types of options to understand their payoffs, and how to construct portfolios with different investment strategies. You'll also derive the famous Black-Scholes equation for pricing options in different contexts, explore exotic options, and calculate risk exposure in a hedging process.

In this module, you'll analyse 4-dimensional spacetime from Special Relativity, gaining skills in tensor algebra and calculus. You'll derive and apply Einstein's equations yourself, modeling black holes or gravitational waves, as you develop your skills in independent thinking, curiosity, and clear communication.

As you work through key concepts, such as nuclear processes, relativity and cosmology, you'll evaluate observational issues like the quest for dark matter. On completion, you'll have the critical thinking and intellectual curiosity to solve real problems modelling cosmic structures.

In this module, you'll use perturbation theory and relevant software, such as MATLAB, to examine equilibria, bifurcation and integrability. You'll build on your understanding from previous modules, such as calculus and computational management, and learn to apply them to problems that exceed the limits of linear systems theory.

Gaining solid knowledge for a career in supply chain management or further study, you'll synthesize new and existing ideas to generate creative solutions to supply chain problems.

Learning about strengths and weaknesses of population sampling and study designs, you will be introduced to appropriate statistical analysis tools including multivariate techniques and modeling data in SPSS. You'll formulate common epidemiological statistics, construct life tables, design clinical trials, and employ multivariate methods, all using tools designed for applied statisticians in health research.

You'll plan your project, gather and synthesize literature, and write a dissertation to present your independent discoveries. You'll then evaluate your own work, and learn to present and discuss your conclusions in writing and through oral presentations.

Through industry case studies, you'll formulate and implement linear, integer programming models for planning and risk analysis. Using industry-standard software, you'll evaluate solutions and communicate data-driven insights tailored for stakeholders. When you complete the module, you'll be able to demonstrate versatile skills in synthesising information, assessing trade-offs and driving impact through evidence-based advice.

From the properties of stars to stellar evolution and the features of our Galaxy, this module will see you utilise interactive computer software to solve astronomical problems.

This module includes a 6 hour compulsory visit to Clanfield Observatory and the South Downs Planetarium to pass this module.

When you complete this module successfully, you'll be able to:

• Apply your understanding of modern astronomical systems to calculations involving photometric and spectroscopic data
• Demonstrate your ability to handle modern astronomical data and compare with astrophysical models
• Apply physical principles of observational probes of cosmology, and solve problems in constraining cosmological parameters

Using freely available modern datasets, you'll learn to select and apply appropriate statistical techniques, using methods such as principal components and clustering. You'll also demonstrate your ability to apply statistical learning techniques in programming languages like R or Python.

You'll learn to model uncertainty in a systematic, mathematical way, ready to apply your subject knowledge across the complexities of social, technological and natural domains.